Blobbed topological recursion
Update: 2013-10-22
Description
Hermitian matrix models have been used since the early days of 2d
quantum gravity, as generating series of discrete surfaces, and
sometimes toy models for string theory. The single trace matrix models
(with measure dM exp( - N Tr V(M)) have been solved in a 1/N expansion
in the 90s by the moment method of Ambjorn et al. Later, Eynard showed
that it can be rewritten more intrinsically in terms of algebraic
geometry of the spectral curve, and formulated the so-called topological
recursion.
quantum gravity, as generating series of discrete surfaces, and
sometimes toy models for string theory. The single trace matrix models
(with measure dM exp( - N Tr V(M)) have been solved in a 1/N expansion
in the 90s by the moment method of Ambjorn et al. Later, Eynard showed
that it can be rewritten more intrinsically in terms of algebraic
geometry of the spectral curve, and formulated the so-called topological
recursion.
In a similar way, we will show that double hermitian matrix models
are solved by the same topological recursion, and more generally, that
arbitrary hermitian matrix models are solved by a "blobbed topological
recursion", whose properties still have to be investigated.
are solved by the same topological recursion, and more generally, that
arbitrary hermitian matrix models are solved by a "blobbed topological
recursion", whose properties still have to be investigated.
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